code: def sdm_monomial_divides(A, B):
      """
      Does there exist a (polynomial) monomial X such that XA = B?
  
      Examples
      ========
  
      Positive examples:
  
      In the following examples, the monomial is given in terms of x, y and the
      generator(s), f_1, f_2 etc. The tuple form of that monomial is used in
      the call to sdm_monomial_divides.
      Note: the generator appears last in the expression but first in the tuple
      and other factors appear in the same order that they appear in the monomial
      expression.
  
      `A = f_1` divides `B = f_1`
  
      >>> from sympy.polys.distributedmodules import sdm_monomial_divides
      >>> sdm_monomial_divides((1, 0, 0), (1, 0, 0))
      True
  
      `A = f_1` divides `B = x^2 y f_1`
  
      >>> sdm_monomial_divides((1, 0, 0), (1, 2, 1))
      True
  
      `A = xy f_5` divides `B = x^2 y f_5`
  
      >>> sdm_monomial_divides((5, 1, 1), (5, 2, 1))
      True
  
      Negative examples:
  
      `A = f_1` does not divide `B = f_2`
  
      >>> sdm_monomial_divides((1, 0, 0), (2, 0, 0))
      False
  
      `A = x f_1` does not divide `B = f_1`
  
      >>> sdm_monomial_divides((1, 1, 0), (1, 0, 0))
      False
  
      `A = xy^2 f_5` does not divide `B = y f_5`
  
      >>> sdm_monomial_divides((5, 1, 2), (5, 0, 1))
      False
      """
      return A[0] == B[0] and all(a <= b for a, b in zip(A[1:], B[1:]))
  
imports: from itertools import permutations
  from sympy.polys.monomials import monomial_mul, monomial_lcm, monomial_div, monomial_deg
  from sympy.polys.polytools import Poly
  from sympy.polys.polyutils import parallel_dict_from_expr
  from sympy.core.singleton import S
  from sympy.core.sympify import sympify
label_desc: Use image node_id 4 for calling a global function with example usage: sdm_monomial_divides(A, B) and returns: unknown